正特征域上格点中的周期调和函数与点计数
代数几何
2009-10-19 v2 谱理论
摘要
本综述讨论了取值于正特征域的格点上的多周期调和函数。作为动机，我们提到了"熄灯"游戏，参考了Sutner、Goldwasser-Klostermeyer-Ware、Barua-Ramakrishnan-Sarkar、Hunzikel-Machiavello-Park等人的工作；另见前两位作者之前的两篇预印本以获取更详细的说明。我们的方法探索了正特征域上的调和分析与代数几何。傅里叶变换使我们能够将格点上调和函数的多周期解释为相应仿射代数簇上点的挠率重阶。
引用
@article{arxiv.0706.2228,
title = {Periodic harmonic functions on lattices and points count in positive characteristic},
author = {Mikhail Zaidenberg},
journal= {arXiv preprint arXiv:0706.2228},
year = {2009}
}
备注
These are notes on 13p. based on a talk presented during the meeting "Analysis on Graphs and Fractals", the Cardiff University, 29 May-2 June 2007 (a sattelite meeting of the programme "Analysis on Graphs and its Applications" at the Isaac Newton Institute from 8 January to 29 June 2007)